{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"低温环境下材料膨胀系数和润滑对望远镜负载扭矩的影响"}]},{"lang":"en","data":[{"name":"text","data":"Effect of material expansion coefficient and lubrication on telescope load torque under low temperature"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"杜","givenname":"福嘉","namestyle":"eastern","prefix":""},{"lang":"en","surname":"DU","givenname":"Fu-jia","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":["first-author"],"bio":[{"lang":"zh","text":["杜福嘉(1975-), 男, 辽宁北票人, 副研究员, 2006年于中科院南京天文光学技术研究所获得硕士学位, 主要从事望远镜控制技术、极端环境影响等方面的研究。E-mail:fjdu@niaot.ac.cn"],"graphic":[],"data":[[{"name":"text","data":"杜福嘉(1975-), 男, 辽宁北票人, 副研究员, 2006年于中科院南京天文光学技术研究所获得硕士学位, 主要从事望远镜控制技术、极端环境影响等方面的研究。E-mail:"},{"name":"text","data":"fjdu@niaot.ac.cn"}]]}],"email":"fjdu@niaot.ac.cn","deceased":false},{"name":[{"lang":"zh","surname":"李","givenname":"朋辉","namestyle":"eastern","prefix":""},{"lang":"en","surname":"LI","givenname":"Peng-hui","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"},{"rid":"aff3","text":"3"}],"role":["corresp"],"corresp":[{"rid":"cor1","lang":"zh","text":"李朋辉(1991-), 男, 河南郑州人, 硕士研究生, 主要从事精密仪器及机械、模态识别与分析等方面的研究。E-mail:yangwangpo@126.com  LI Peng-hui, E-mail: yangwangpo@126.com ","data":[{"name":"text","data":"李朋辉(1991-), 男, 河南郑州人, 硕士研究生, 主要从事精密仪器及机械、模态识别与分析等方面的研究。E-mail:yangwangpo@126.com  LI Peng-hui, E-mail: yangwangpo@126.com "}]}],"email":"yangwangpo@126.com","deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"中国科学院 国家天文台 南京天文光学技术研究所, 江苏 南京 210042","data":[{"name":"text","data":"中国科学院 国家天文台 南京天文光学技术研究所, 江苏 南京 210042"}]},{"lang":"en","label":"1","text":"National Astronomical Observatories/Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, China","data":[{"name":"text","data":"National Astronomical Observatories/Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"中国科学院 天文光学技术重点实验室, 江苏 南京 210042","data":[{"name":"text","data":"中国科学院 天文光学技术重点实验室, 江苏 南京 210042"}]},{"lang":"en","label":"2","text":"Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, China","data":[{"name":"text","data":"Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, China"}]}]},{"id":"aff3","intro":[{"lang":"zh","label":"3","text":"中国科学院大学, 北京 100049","data":[{"name":"text","data":"中国科学院大学, 北京 100049"}]},{"lang":"en","label":"3","text":"University of Chinese Academy of Sciences, Beijing 100049, China","data":[{"name":"text","data":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"为了深入研究望远镜的负载扭矩随着温度降低而增大的机理，提高低温下伺服系统的跟踪精度。首先分析了轴承摩擦扭矩的各种影响因素和低温对负载扭矩的影响，研究了润滑剂黏度随温度的变化规律，试验对比了有无添加润滑脂情况下负载扭矩的变化，结果表明在低温下无润滑脂时负载扭矩的波动减少并且线性度提高。其次分析了轴承摩擦扭矩和间隙的关系，采用电阻应变片法测量不同材料在不同温度下的热膨胀系数，建立起材料膨胀系数和扭矩的相关特性，结果表明低温下负载扭矩是常温下的6.67倍，而材料尺寸的最大缩短量达到960 "},{"name":"italic","data":[{"name":"text","data":"μ"}]},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"text","data":"。通过对低温负载扭矩机理的研究，可为低温环境下望远镜的精确控制提供理论和试验数据。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"In order to improve the accuracy of the servo system at low temperature, the mechanism that the load torque of the telescope increase along with the temperature decrease must be deeply understood. Firstly, the influence factors of friction torque of bearing and the influence of low temperature on load torque were analyzed. The lubricant viscosity with temperature variation was studied. The relationship between load torque and grease was tested and discussed. The results indicate that the fluctuation of load torque without the grease at low temperature is decreased and the linearity of load torque is increased. The influence of clearance on bearing friction torque was also analyzed. The expansion coefficient of different materials at different temperatures was measured by resistance strain gauge method. The correlation coefficient between torque and material expansion was established. The result indicates that the load torque at low temperature is 6.67 times load torque at normal temperature, and the maximum of shortening of material reaches 960 "},{"name":"italic","data":[{"name":"text","data":"μ"}]},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"text","data":". The research on the mechanism of cryogenic load torque in this paper can provide theoretical and experimental data for the precise control of the telescope under extreme environment."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"望远镜"}],[{"name":"text","data":"低温环境"}],[{"name":"text","data":"摩擦扭矩"}],[{"name":"text","data":"热膨胀系数"}],[{"name":"text","data":"润滑脂"}]]},{"lang":"en","data":[[{"name":"text","data":"telescope"}],[{"name":"text","data":"low temperature environment"}],[{"name":"text","data":"friction torque"}],[{"name":"text","data":"thermal expansion coefficient"}],[{"name":"text","data":"grease"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"1"}],"title":[{"name":"text","data":"引言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"随着天文观测的深入，天文望远镜已深入到南极内陆地区，南极内陆地区的最低温度可达-80 ℃，在低温环境下传动系统由于润滑、间隙、材料特性等因素的影响，导致望远镜的负载扭矩增大并具有非线性特性，极端情况下甚至超过电机的峰值扭矩从而卡死传动系统。地基望远镜在跟踪天体目标时转速非常低，负载扭矩的非线性和波动会使望远镜跟踪时出现低速爬行、稳态误差等现象，最终导致望远镜的控制精度降低"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。为了使望远镜能够在低温环境下高精度运行，迫切需要研究低温下望远镜负载扭矩增大的机理和影响因素，从而有针对性地提出解决方案。"}]},{"name":"p","data":[{"name":"text","data":"在恒速跟踪时，望远镜的负载扭矩主要由轴系摩擦引起的摩擦扭矩组成。影响摩擦扭矩的因素众多，主要有望远镜的速度、加速度、温度、湿度、接触材料特性、润滑条件、压力以及表面形貌等，因此，摩擦扭矩常常带有非线性因素"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"2","type":"bibr","rid":"b2","data":[{"name":"text","data":"2"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。目前在伺服系统中，对摩擦扭矩的研究主要通过分析系统外特性，并据此对摩擦进行识别、分类和建模。何秋生等结合Dahl模型和LuGre模型提出了一种改进的模型，并通过仿真验证了模型的有效性"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。方群玲等研究了载荷和转速对模型参数和轴承润滑的关系"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"3","type":"bibr","rid":"b3","data":[{"name":"text","data":"3"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。廖洪波等通过非线性参数辨识了LuGre摩擦模型的静态和动态参数"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"4","type":"bibr","rid":"b4","data":[{"name":"text","data":"4"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。曾德林等通过分布辨识方法辨识了LuGre摩擦参数"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"5","type":"bibr","rid":"b5","data":[{"name":"text","data":"5"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"研究摩擦扭矩外特性并采取前馈补偿措施可以减少摩擦扭矩非线性对系统的影响，提高系统的控制精度。但是外界环境对外特性有显著影响，为深入理解外界环境对负载扭矩的影响，需要建立影响因素和负载扭矩之间的量化关系。目前，对低温环境下负载扭矩的研究工作不多，而且主要从结构设计和材料选择角度克服低温的影响。为了应对低温环境的影响，目前在南极和空间设备上主要采取的措施是被动温控、优选器件和隔离"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"6","type":"bibr","rid":"b6","data":[{"name":"text","data":"6"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"8","type":"bibr","rid":"b8","data":[{"name":"text","data":"8"}]}}],"rid":["b6","b7","b8"],"text":"6-8","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。在影响望远镜负载扭矩的各种因素中，轴承摩擦扭矩占据主导地位。国内外学者对轴承摩擦扭矩开展了比较深入的研究。张学宁等通过简化Jones-Harris方法分析了负荷和内圈偏转角等不同因素对接触角的影响并通过试验进行了验证"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"9","type":"bibr","rid":"b9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。方斌等利用Jones-Harris模型提高了模型求解效率并通过载荷消除了接触角分布的不一致性"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"10","type":"bibr","rid":"b10","data":[{"name":"text","data":"10"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。魏波等研究了角接触轴承在联合载荷作用下的混合润滑问题，得出了载荷和转速与油膜的关系"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"11","type":"bibr","rid":"b11","data":[{"name":"text","data":"11"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。Ianus通过试验测定了不同转速下推力球轴承的摩擦扭矩，并与理论分析结果进行了对比测试，验证了测试结果的准确性"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"12","type":"bibr","rid":"b12","data":[{"name":"text","data":"12"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"为了得到更好的成像质量，望远镜在跟踪恒星的过程中要求达到0.1″的跟踪精度，高跟踪精度要求轴系运转平稳且刚度高。如果轴承游隙过大，虽然可以减少摩擦阻力，却会导致接触应力增大、易产生径向跳动并引起振动和噪声，最终降低跟踪精度。本文着眼于现有望远镜的传动系统，重点研究了润滑脂和材料膨胀系数对望远镜负载扭矩的影响，并分析这两种因素的影响规律，为低温环境下望远镜控制精度的提高提供参考。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"低温对传动系统负载扭矩的影响"}],"level":"1","id":"s2"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.1"}],"title":[{"name":"text","data":"轴承摩擦扭矩分析"}],"level":"2","id":"s2-1"}},{"name":"p","data":[{"name":"text","data":"摩擦现象一般通过不同的摩擦模型来精确描述，其中描述负载动静摩擦特性与速度之间关系的Stribeck摩擦模型是最为常用的。"}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"1"}],"data":[{"name":"text","data":" 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"},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706985&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706985&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706985&type=middle"}}}],"id":"gxjmgc-26-3-616-E1"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"sub","data":[{"name":"text","data":"c"}]},{"name":"text","data":"为库仑摩擦力矩；"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"sub","data":[{"name":"text","data":"s"}]},{"name":"text","data":"为最大静摩擦力矩；"},{"name":"italic","data":[{"name":"text","data":"B"}]},{"name":"text","data":"为黏滞摩擦系数；"},{"name":"italic","data":[{"name":"text","data":"ω"}]},{"name":"text","data":"为角速度；sgn为符号函数；"},{"name":"italic","data":[{"name":"text","data":"v"}]},{"name":"sub","data":[{"name":"text","data":"s"}]},{"name":"text","data":"为Stribeck速度；"},{"name":"italic","data":[{"name":"text","data":"δ"}]},{"name":"sub","data":[{"name":"text","data":"vs"}]},{"name":"text","data":"为控制曲线形状。Stribeck模型主要描述了摩擦力矩"},{"name":"italic","data":[{"name":"text","data":"M"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"v"}]},{"name":"text","data":")与转速"},{"name":"italic","data":[{"name":"text","data":"v"}]},{"name":"text","data":"之间的关系，但是该模型没有量化外界环境对摩擦力矩的影响。在温度变化较大的环境中，环境温度对摩擦力矩的影响不可忽视，为了深入了解摩擦力矩和波动的影响因素，需要了解轴承摩擦力矩与外界环境的关系。在中小型望远镜中，滚动轴承获得了广泛应用"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"10","type":"bibr","rid":"b10","data":[{"name":"text","data":"10"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。组成滚动轴承的各个部件在运动过程中因相互作用会产生摩擦，并且摩擦力矩的大小与预紧和工作载荷紧密相关"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"13","type":"bibr","rid":"b13","data":[{"name":"text","data":"13"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。在工程实践中, 滚动轴承的摩擦力矩通常采用Harris经验公式计算，Harris公式为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"2"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706992&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706992&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706992&type=middle"}}}],"id":"gxjmgc-26-3-616-E2"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"M"}]},{"name":"text","data":"为摩擦力矩；"},{"name":"italic","data":[{"name":"text","data":"d"}]},{"name":"text","data":"为钢球直径；"},{"name":"italic","data":[{"name":"text","data":"P"}]},{"name":"text","data":"为负荷；"},{"name":"italic","data":[{"name":"text","data":"f"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"为轴承系数，与负荷以及轴承形式相关；"},{"name":"italic","data":[{"name":"text","data":"r"}]},{"name":"text","data":"为润滑剂的动黏性系数；"},{"name":"italic","data":[{"name":"text","data":"f"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"为与轴承形式和润滑方式相关的系数；"},{"name":"italic","data":[{"name":"text","data":"n"}]},{"name":"text","data":"为轴承转速。从公式(2)可以看出，对于同一轴承，轴承的摩擦扭矩主要和承受的负荷、润滑剂的黏度以及轴承本身的材料、表面状况形式相关。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.2"}],"title":[{"name":"text","data":"低温对轴承摩擦扭矩的影响"}],"level":"2","id":"s2-2"}},{"name":"p","data":[{"name":"text","data":"低温对望远镜传动系统的影响主要表现为低温下扭矩会增大。"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"是实测的望远镜轴系负载扭矩随温度的变化曲线，图中红色曲线为温度曲线，蓝色曲线为负载曲线。所测传动系统由永磁同步电机、行星齿轮减速机和负载平台组成，电机为瑞诺公司的BLS 30电机，电机轴承为深沟球轴承，轴承尺寸为外径16 mm，内径8 mm。摩擦扭矩通过力矩平衡原理测量，力矩平衡方程为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"3"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706999&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706999&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1706999&type=middle"}}}],"id":"gxjmgc-26-3-616-E3"}}]},{"name":"fig","data":{"id":"Figure1","caption":[{"lang":"zh","label":[{"name":"text","data":"图1"}],"title":[{"name":"text","data":"负载扭矩随温度的变化曲线"}]},{"lang":"en","label":[{"name":"text","data":"Fig 1"}],"title":[{"name":"text","data":"Load torque "},{"name":"italic","data":[{"name":"text","data":"vs"}]},{"name":"text","data":". temperature"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707006&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707006&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707006&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"为电机驱动扭矩；"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"sub","data":[{"name":"text","data":"f"}]},{"name":"text","data":"为摩擦扭矩；"},{"name":"italic","data":[{"name":"text","data":"J"}]},{"name":"text","data":"为转动惯量；"},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707158&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707158&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707158&type=middle"}}}]},{"name":"text","data":"为角加速度；"},{"name":"italic","data":[{"name":"text","data":"ω"}]},{"name":"sub","data":[{"name":"text","data":"m"}]},{"name":"text","data":"为角速度。电机输出扭矩"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"="},{"name":"italic","data":[{"name":"text","data":"K"}]},{"name":"sub","data":[{"name":"text","data":"t"}]},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"K"}]},{"name":"sub","data":[{"name":"text","data":"t"}]},{"name":"text","data":"为电机扭矩系数，"},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"为电机输出电流。则摩擦扭矩可表示为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"4"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707015&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707015&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707015&type=middle"}}}],"id":"gxjmgc-26-3-616-E4"}}]},{"name":"p","data":[{"name":"text","data":"对于一台电机"},{"name":"italic","data":[{"name":"text","data":"K"}]},{"name":"text","data":"  "},{"name":"sub","data":[{"name":"text","data":"t"}]},{"name":"text","data":"是常数，因此只要测得输出电流"},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"和转台加速度"},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707164&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707164&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707164&type=middle"}}}]},{"name":"text","data":"，便可获得摩擦力矩"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"sub","data":[{"name":"text","data":"f"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"从"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"可以看出，随着温度的降低，传动系统的负载扭矩不断增大，并且具有非线性特性。常温下的负载扭矩为30 mN·m，而在-80 ℃环境温度时，负载扭矩增加到了200 mN·m，是常温下的6.67倍。实际工程中的电机过载系数是一定的，低温下负载扭矩增大和非线性特性不但会引起跟踪精度的降低，严重时甚至会超过伺服电机的峰值扭矩进而卡死系统。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3"}],"title":[{"name":"text","data":"润滑脂对负载扭矩的影响"}],"level":"1","id":"s3"}},{"name":"p","data":[{"name":"text","data":"良好的润滑可以减少摩擦，并且提高轴承的寿命与可靠性。在低温环境中，润滑脂的流变特性是影响润滑脂性能的重要参数"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"11","type":"bibr","rid":"b11","data":[{"name":"text","data":"11"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。润滑脂的流变特性通常用Herschel-Bulkley流变模型来表示："},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707170&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707170&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707170&type=middle"}}}]},{"name":"text","data":"，其中"},{"name":"italic","data":[{"name":"text","data":"τ"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"为屈服应力，"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"text","data":"为稠度系数，"},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707177&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707177&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707177&type=middle"}}}]},{"name":"text","data":"为剪切速率，"},{"name":"italic","data":[{"name":"text","data":"n"}]},{"name":"text","data":"为剪切变稀指数。随着温度的降低，润滑脂的稠度系数"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"text","data":"和屈服应力"},{"name":"italic","data":[{"name":"text","data":"τ"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"增大，从而剪切应力"},{"name":"italic","data":[{"name":"text","data":"τ"}]},{"name":"text","data":"加大，最终使润滑脂黏度增大。润滑脂的动力黏度为"},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707186&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707186&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707186&type=middle"}}}]},{"name":"text","data":"，式中"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"text","data":"为绝对温度；"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"text","data":"为玻尔兹曼常数；"},{"name":"italic","data":[{"name":"text","data":"V"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"V"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"为活化体积；"},{"name":"italic","data":[{"name":"text","data":"E"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"为表观活化能；"},{"name":"italic","data":[{"name":"text","data":"p"}]},{"name":"text","data":"为压力；"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"text","data":"为常数。润滑脂的黏度增加，导致润滑脂流动过程的内摩擦阻力增大，需要借助足够的外力来克服由此产生的阻力，从而直接导致负载扭矩上升。"}]},{"name":"p","data":[{"name":"text","data":"为深入了解润滑脂对负载扭矩的影响程度，对比研究了有无润滑脂时负载扭矩的变化情况。"},{"name":"xref","data":{"text":"图 2","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2"}]}},{"name":"text","data":"是同一减速机有无润滑脂时的负载扭矩随温度的变化曲线，"},{"name":"xref","data":{"text":"图 2","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2"}]}},{"name":"text","data":"中上图是减速机加入润滑脂时负载扭矩随温度的变化曲线。"},{"name":"xref","data":{"text":"图 2","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2"}]}},{"name":"text","data":"中下图是减速机清洗掉润滑脂之后负载扭矩随温度的变化曲线。从中可以看出，减速机添加润滑脂后，当温度降到-60 ℃以后，负载扭矩已经大于电机的拖动扭矩，电机出现卡死情况；而去掉减速机的润滑脂之后，虽然负载扭矩随温度的降低还是增大，但是即使在-60 ℃以下，电机依然可以拖动负载，并没有出现电机卡死的问题。此外，从负载曲线可以看出，添加润滑脂时负载的波动较大，即在同一温度点上负载的最大值和最小值的差值较大。以-40 ℃温度点为例，加入润滑脂的轴承扭矩的均方差为18 mN·m，而清除掉润滑脂之后的轴承扭矩的均方差为16 mN·m。"}]},{"name":"fig","data":{"id":"Figure2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"加和不加润滑脂时的负载扭矩"}]},{"lang":"en","label":[{"name":"text","data":"Fig 2"}],"title":[{"name":"text","data":"Load torque with and without grease"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707021&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707021&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707021&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"为了更好理解润滑脂对负载扭矩的影响，特对负载曲线进行60阶的最小二乘曲线拟合，曲线拟合后如"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"所示。从拟合后的曲线可以看出：(1)清除润滑脂的负载曲线对称性好，而加入润滑脂的轴承其负载扭矩在温度下降和上升时曲线不对称，这说明润滑脂在温度变化过程中由于黏度变化的滞后性对负载有非线性影响；(2)在各个温度点不添加润滑脂比添加润滑脂的负载扭矩明显有所降低；(3)在-67 ℃的低温下，不添加润滑脂的电机没有因为负载扭矩超过电机峰值扭矩而出现卡死问题，电机还能正常运转。"}]},{"name":"fig","data":{"id":"Figure3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"曲线拟合后负载扭矩对比"}]},{"lang":"en","label":[{"name":"text","data":"Fig 3"}],"title":[{"name":"text","data":"Comparison of load torque after curve fitting"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707026&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707026&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707026&type=middle"}]}}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4"}],"title":[{"name":"text","data":"材料的热胀冷缩对负载扭矩的影响"}],"level":"1","id":"s4"}},{"name":"p","data":[{"name":"text","data":"从润滑脂对负载特性的影响可以看出，即使排除了润滑脂对负载扭矩的影响，由于温度降低导致传动系统尺寸的改变也会使负载扭矩增加6.67倍。这主要是由于温度降低导致轴承材料的尺寸变化量不同，使轴承工作游隙减小，进而引起弹性变形和接触载荷增大，最终使负载扭矩增大。"}]},{"name":"p","data":[{"name":"text","data":"温度对轴承工作游隙的影响主要是由内、外圈过盈量的变化和温度差异所导致的各零件膨胀量不一致造成的。工作游隙的变化量可由轴承内滚道膨胀量"},{"name":"italic","data":[{"name":"text","data":"ΔP"}]},{"name":"sub","data":[{"name":"text","data":"ti"}]},{"name":"text","data":"、外滚道膨胀量"},{"name":"italic","data":[{"name":"text","data":"ΔP"}]},{"name":"sub","data":[{"name":"text","data":"to"}]},{"name":"text","data":"及钢球膨胀量"},{"name":"italic","data":[{"name":"text","data":"ΔP"}]},{"name":"sub","data":[{"name":"text","data":"tr"}]},{"name":"text","data":"来表示："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"5"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707029&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707029&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707029&type=middle"}}}],"id":"gxjmgc-26-3-616-E5"}}]},{"name":"p","data":[{"name":"text","data":"工作游隙由于套圈的膨胀差引起的减小量"},{"name":"italic","data":[{"name":"text","data":"ΔY"}]},{"name":"text","data":"可表示为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"6"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707036&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707036&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707036&type=middle"}}}],"id":"gxjmgc-26-3-616-E6"}}]},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"italic","data":[{"name":"text","data":"α"},{"name":"sub","data":[{"name":"text","data":"b"}]}]},{"name":"text","data":"为轴承的线膨胀系数；"},{"name":"italic","data":[{"name":"text","data":"Δt"}]},{"name":"text","data":"为内圈和外圈的温度差；"},{"name":"italic","data":[{"name":"text","data":"D"}]},{"name":"sub","data":[{"name":"text","data":"e"}]},{"name":"text","data":"为套圈滚道直径。"}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"7"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707045&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707045&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707045&type=middle"}}}],"id":"gxjmgc-26-3-616-E7"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"R"}]},{"name":"text","data":"为套圈沟槽的曲率半径，"},{"name":"italic","data":[{"name":"text","data":"r"}]},{"name":"text","data":"为钢球半径。由式(7)可知, 工作游隙"},{"name":"italic","data":[{"name":"text","data":"Y"}]},{"name":"text","data":"的减小会导致轴承的接触角"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"增大在低速条件下，钢球与内、外滚道接触角的改变影响到接触变形，最终影响到载荷的分布。"}]},{"name":"p","data":[{"name":"text","data":"根据文献["},{"name":"xref","data":{"text":"11","type":"bibr","rid":"b11","data":[{"name":"text","data":"11"}]}},{"name":"text","data":"]，接触角的变化关系为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"8"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707054&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707054&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707054&type=middle"}}}],"id":"gxjmgc-26-3-616-E8"}}]},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"text","data":"为轴承载荷分布范围参数；"},{"name":"italic","data":[{"name":"text","data":"J"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"为轴向积分；"},{"name":"italic","data":[{"name":"text","data":"Z"}]},{"name":"text","data":"为钢球数量；"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"a"}]},{"name":"text","data":"为轴向载荷；"},{"name":"italic","data":[{"name":"text","data":"D"}]},{"name":"sub","data":[{"name":"text","data":"w"}]},{"name":"text","data":"为钢球直径；"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"text","data":"为接触变形系数；"},{"name":"italic","data":[{"name":"text","data":"f"}]},{"name":"sub","data":[{"name":"text","data":"m"}]},{"name":"text","data":"为曲率比平均值。"}]},{"name":"p","data":[{"name":"text","data":"根据赫兹接触理论，深沟球轴承的接触应力"},{"name":"italic","data":[{"name":"text","data":"P"}]},{"name":"sub","data":[{"name":"text","data":"m"}]},{"name":"text","data":"为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"9"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707060&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707060&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707060&type=middle"}}}],"id":"gxjmgc-26-3-616-E9"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"e"},{"name":"sub","data":[{"name":"text","data":"a"}]}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"e"},{"name":"sub","data":[{"name":"text","data":"b"}]}]},{"name":"text","data":"分别为赫兹接触系数；∑"},{"name":"italic","data":[{"name":"text","data":"ρ"}]},{"name":"text","data":"为主曲率和；"},{"name":"italic","data":[{"name":"text","data":"Q"}]},{"name":"text","data":"为轴承总负荷，"},{"name":"italic","data":[{"name":"text","data":"Q"}]},{"name":"text","data":"可表示为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"10"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707066&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707066&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707066&type=middle"}}}],"id":"gxjmgc-26-3-616-E10"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"r"}]},{"name":"text","data":"为轴承所承受的径向载荷，"},{"name":"italic","data":[{"name":"text","data":"Z"}]},{"name":"text","data":"为滚动体个数。接触角和工作间隙的改变直接导致负荷增大，最终使负载扭矩增大。"}]},{"name":"p","data":[{"name":"text","data":"在望远镜轴系中，轴承和外壳所用的材料是不同的，环境温度变化时，不同材料热膨胀系数的差异会导致间隙的缩小。即使是同一种材料，由于部件尺寸的不同，热膨胀系数导致的伸缩量不同，也会导致负载扭矩的上升。为了量化轴承间隙和负载扭矩之间的关系，掌握不同温度下材料的热膨胀系数至关重要。"}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4.1"}],"title":[{"name":"text","data":"材料热膨胀系数测量原理"}],"level":"2","id":"s4-1"}},{"name":"p","data":[{"name":"text","data":"热膨胀系数是材料的一个基础物理参数，通用材料在常温下的膨胀系数可以在机械手册或材料手册中查到。但是对于特别低温的场合，由于实际应用不多，相关的热膨胀系数数据较少，需要通过实测获取材料在低温下的热膨胀系数。在各种测试热膨胀系数的方法中，应变片法对环境温度的均匀性需求较低，因此选用应变片的方式测量材料的热膨胀系数。"}]},{"name":"p","data":[{"name":"text","data":"电阻应变片通过金属电阻丝的应变效应来完成参数测量，由金属丝物理尺寸改变引起的电阻相对变化量为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"11"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707072&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707072&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707072&type=middle"}}}],"id":"gxjmgc-26-3-616-E11"}}]},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"italic","data":[{"name":"text","data":"λ"}]},{"name":"text","data":"为压阻系数；"},{"name":"italic","data":[{"name":"text","data":"μ"}]},{"name":"text","data":"为泊松比；"},{"name":"italic","data":[{"name":"text","data":"E"}]},{"name":"text","data":"为弹性模量；"},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"text","data":"为应变。对于特定的材料，(1+2"},{"name":"italic","data":[{"name":"text","data":"μ"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"λE"}]},{"name":"text","data":")是一常数。一般令(1+2"},{"name":"italic","data":[{"name":"text","data":"μ"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"λE"}]},{"name":"text","data":")="},{"name":"italic","data":[{"name":"text","data":"K"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，则有"},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707192&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707192&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707192&type=middle"}}}]},{"name":"text","data":"="},{"name":"italic","data":[{"name":"text","data":"K"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"电阻应变片测量材料膨胀系数的原理是：把应变片贴到被测材料的表面，当环境温度变化时，由于电阻应变片与被测物体的伸缩量不同而产生应变，从而引起应变片的电阻值发生变化。此外，应变片的敏感栅由金属电阻箔组成，应变片自身电阻的温度系数也会导致电阻值的变化。因此，总的电阻变化"},{"name":"italic","data":[{"name":"text","data":"ΔR"}]},{"name":"text","data":"为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"12"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707081&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707081&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707081&type=middle"}}}],"id":"gxjmgc-26-3-616-E12"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"sub","data":[{"name":"text","data":"G"}]},{"name":"text","data":"为应变片的温度系数；"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"s"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"G"}]},{"name":"text","data":"分别为被测物体和应变片的热膨胀系数；"},{"name":"italic","data":[{"name":"text","data":"ΔT"}]},{"name":"text","data":"为温度变化量。则应变片在被测材料上的应变量"},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"sub","data":[{"name":"text","data":"G/S"}]},{"name":"text","data":"为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"13"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707093&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707093&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707093&type=middle"}}}],"id":"gxjmgc-26-3-616-E13"}}]},{"name":"p","data":[{"name":"text","data":"由于在式(13)中，"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"sub","data":[{"name":"text","data":"G"}]},{"name":"text","data":"和("},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"S"}]},{"name":"text","data":"－"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"G"}]},{"name":"text","data":")都不是线性的，因此无法直接通过测量电阻应变片的应变得到材料的膨胀系数。为了消除应变片自身电阻温度系数对测量结果的影响，测量系统如"},{"name":"xref","data":{"text":"图 4","type":"fig","rid":"Figure4","data":[{"name":"text","data":"图 4"}]}},{"name":"text","data":"所示，把相同的两片应变片分别贴到被测材料和参考材料上。被测材料的热膨胀系数"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"S"}]},{"name":"text","data":"未知，而参考材料的热膨胀系数"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"R"}]},{"name":"text","data":"已知，则可以得到参考材料上应变片的应变量为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"14"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707102&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707102&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707102&type=middle"}}}],"id":"gxjmgc-26-3-616-E14"}}]},{"name":"fig","data":{"id":"Figure4","caption":[{"lang":"zh","label":[{"name":"text","data":"图4"}],"title":[{"name":"text","data":"热膨胀系数测量电路图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 4"}],"title":[{"name":"text","data":"Thermal expansion coefficient measuring circuit"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707110&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707110&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707110&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"式(13)减去式(14)，得到:"}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"15"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707118&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707118&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707118&type=middle"}}}],"id":"gxjmgc-26-3-616-E15"}}]},{"name":"p","data":[{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"sub","data":[{"name":"text","data":"G/S"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"ε"}]},{"name":"sub","data":[{"name":"text","data":"G/R"}]},{"name":"text","data":"这两个参数可以使用应变数据采集仪直接测量到，因此，在已知参考材料的热膨胀系数"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"sub","data":[{"name":"text","data":"R"}]},{"name":"text","data":"下，材料的热膨胀系数可以通过测量在被测材料和参考材料上的应变量并通过式(15)得到。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4.2"}],"title":[{"name":"text","data":"膨胀系数对负载扭矩的影响"}],"level":"2","id":"s4-2"}},{"name":"p","data":[{"name":"text","data":"为了精确测定望远镜轴系不同材料的热膨胀系数，特搭建测试系统如"},{"name":"xref","data":{"text":"图 5","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5"}]}},{"name":"text","data":"所示，所测轴承内径为460 mm，外径为620 mm。在轴承的外圈、内圈、平台外壳上分别贴上电阻应变片，选用MM公司的TSB-1硅酸钛玻璃作为参考材料，其膨胀系数为(0.00±0.015)×10"},{"name":"sup","data":[{"name":"text","data":"-6"}]},{"name":"text","data":"/℃@(5~35 ℃)。TSB-1材料是一种由康宁公司生产的超低膨胀玻璃(ULE, Ultra Low Expansion glass)，它在-100~200 ℃下热膨胀系数的典型值是(-0.03±0.03)×10"},{"name":"sup","data":[{"name":"text","data":"-6"}]},{"name":"text","data":"/℃。相对于所测试材料的热膨胀系数，TSB-1是理想的参考材料。在轴承内圈、外圈和外壳上分别粘贴应变片，并与贴在TSB-1上的应变片成组测量。应变片栅长6.35 mm，栅宽2.54 mm，工作基长13.2 mm，工作基宽5.6 mm。在轴承内圈、轴承外圈、外壳上分别贴上热电偶温度传感器。把平台整体放入低温箱内，连续记录温度和应变数据，采样周期为10 s。"}]},{"name":"fig","data":{"id":"Figure5","caption":[{"lang":"zh","label":[{"name":"text","data":"图5"}],"title":[{"name":"text","data":"热膨胀系数测试系统"}]},{"lang":"en","label":[{"name":"text","data":"Fig 5"}],"title":[{"name":"text","data":"Test system of thermal expansion coefficient"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707126&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707126&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707126&type=middle"}]}},{"name":"p","data":[{"name":"xref","data":{"text":"图 6","type":"fig","rid":"Figure6","data":[{"name":"text","data":"图 6"}]}},{"name":"text","data":"是3个测点的应变随温度的变化曲线和测试温度曲线，其中#2和#3是轴承内外圈的应变曲线，#4是轴承外壳的应变曲线。整个测试过程中的最低温度是-66.7 ℃，从温度曲线可以看出，轴承内外圈和外壳的温度是一致的，这样可以排除因为温度差异导致的测量误差。从"},{"name":"xref","data":{"text":"图 6","type":"fig","rid":"Figure6","data":[{"name":"text","data":"图 6"}]}},{"name":"text","data":"可以看出，随着温度的降低，各个点的应变量为负值并不断增大，因此，所测材料在温度降低时不断缩短，最大应变达到了960 "},{"name":"italic","data":[{"name":"text","data":"με"}]},{"name":"text","data":"。但是各个点的应变增加量又有所不同，其中外壳和轴承材料的应变量明显不同。各个点增加量如"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure6","caption":[{"lang":"zh","label":[{"name":"text","data":"图6"}],"title":[{"name":"text","data":"应变随温度的变化曲线"}]},{"lang":"en","label":[{"name":"text","data":"Fig 6"}],"title":[{"name":"text","data":"Strain "},{"name":"italic","data":[{"name":"text","data":"vs"}]},{"name":"text","data":". temperature"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707133&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707133&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707133&type=middle"}]}},{"name":"table","data":{"id":"Table1","caption":[{"lang":"zh","label":[{"name":"text","data":"表1"}],"title":[{"name":"text","data":"不同点在不同温度下的应变量"}]},{"lang":"en","label":[{"name":"text","data":"Table 1"}],"title":[{"name":"text","data":"Strain of different points at different temperatures"}]}],"note":[],"table":[{"head":[[{"rowspan":"2","align":"center","style":"class:table_top_border","data":[{"name":"text","data":"温度/℃"}]},{"colspan":"3","align":"center","style":"class:table_top_border","data":[{"name":"text","data":"应变增加量/"},{"name":"italic","data":[{"name":"text","data":"με"}]}]}],[{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"轴承内圈"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"轴承外圈"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"外壳"}]}]],"body":[[{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"-20"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"136"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"137"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"116"}]}],[{"align":"center","data":[{"name":"text","data":"-30"}]},{"align":"center","data":[{"name":"text","data":"118"}]},{"align":"center","data":[{"name":"text","data":"118"}]},{"align":"center","data":[{"name":"text","data":"104"}]}],[{"align":"center","data":[{"name":"text","data":"-40"}]},{"align":"center","data":[{"name":"text","data":"117"}]},{"align":"center","data":[{"name":"text","data":"117"}]},{"align":"center","data":[{"name":"text","data":"101"}]}],[{"align":"center","data":[{"name":"text","data":"-50"}]},{"align":"center","data":[{"name":"text","data":"113"}]},{"align":"center","data":[{"name":"text","data":"114"}]},{"align":"center","data":[{"name":"text","data":"98"}]}],[{"align":"center","data":[{"name":"text","data":"-60"}]},{"align":"center","data":[{"name":"text","data":"129"}]},{"align":"center","data":[{"name":"text","data":"109"}]},{"align":"center","data":[{"name":"text","data":"118"}]}],[{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"-66.7"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"78"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"70"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"68"}]}]],"foot":[]}]}},{"name":"p","data":[{"name":"xref","data":{"text":"图 7","type":"fig","rid":"Figure7","data":[{"name":"text","data":"图 7"}]}},{"name":"text","data":"是各个点材料的热膨胀系数和温度的关系曲线(彩图见期刊电子版)。其中红色曲线是环境温度曲线，温度为2~-67 ℃，其余三条曲线是不同材料的热膨胀系数在不同时间的变化曲线。从"},{"name":"xref","data":{"text":"图 7","type":"fig","rid":"Figure7","data":[{"name":"text","data":"图 7"}]}},{"name":"text","data":"可以看出，轴承和外壳材料的热膨胀系数不同，在常温下，轴承材料的热膨胀系数为12×10"},{"name":"sup","data":[{"name":"text","data":"-6"}]},{"name":"text","data":"/℃，外壳材料的热膨胀系数为10.5×10"},{"name":"sup","data":[{"name":"text","data":"-6"}]},{"name":"text","data":"/℃。此外，在温度下降过程中，-60 ℃之前，材料的热膨胀系数基本保持不变，当环境温度低于-60 ℃，材料的热膨胀系数明显增大。"},{"name":"xref","data":{"text":"表 2","type":"table","rid":"Table2","data":[{"name":"text","data":"表 2"}]}},{"name":"text","data":"列出了不同温度下的材料热膨胀系数。"}]},{"name":"fig","data":{"id":"Figure7","caption":[{"lang":"zh","label":[{"name":"text","data":"图7"}],"title":[{"name":"text","data":"材料膨胀系数与温度的关系曲线"}]},{"lang":"en","label":[{"name":"text","data":"Fig 7"}],"title":[{"name":"text","data":"Thermal expansion coefficient "},{"name":"italic","data":[{"name":"text","data":"vs."}]},{"name":"text","data":" temperature"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707141&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707141&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707141&type=middle"}]}},{"name":"table","data":{"id":"Table2","caption":[{"lang":"zh","label":[{"name":"text","data":"表2"}],"title":[{"name":"text","data":"不同温度区间的材料热膨胀系数"}]},{"lang":"en","label":[{"name":"text","data":"Table 2"}],"title":[{"name":"text","data":"Thermal expansion coefficients at different temperature ranges"}]}],"note":[],"table":[{"head":[[{"rowspan":"2","align":"center","style":"class:table_top_border","data":[{"name":"text","data":"温度范围"},{"name":"text","data":""},{"name":"text","data":"/℃"}]},{"colspan":"3","align":"center","style":"class:table_top_border","data":[{"name":"text","data":"平均膨胀系数(×10"},{"name":"sup","data":[{"name":"text","data":"-6"}]},{"name":"text","data":"/℃)"}]}],[{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"轴承内圈"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"轴承外圈"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"轴承外壳"}]}]],"body":[[{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"2~-10"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"12.182"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"12.018"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"10.575"}]}],[{"align":"center","data":[{"name":"text","data":"-10~-20"}]},{"align":"center","data":[{"name":"text","data":"12.072"}]},{"align":"center","data":[{"name":"text","data":"11.893"}]},{"align":"center","data":[{"name":"text","data":"10.474"}]}],[{"align":"center","data":[{"name":"text","data":"-20~-30"}]},{"align":"center","data":[{"name":"text","data":"11.974"}]},{"align":"center","data":[{"name":"text","data":"11.790"}]},{"align":"center","data":[{"name":"text","data":"10.379"}]}],[{"align":"center","data":[{"name":"text","data":"-30~-40"}]},{"align":"center","data":[{"name":"text","data":"11.920"}]},{"align":"center","data":[{"name":"text","data":"11.768"}]},{"align":"center","data":[{"name":"text","data":"10.334"}]}],[{"align":"center","data":[{"name":"text","data":"-40~-50"}]},{"align":"center","data":[{"name":"text","data":"11.851"}]},{"align":"center","data":[{"name":"text","data":"11.767"}]},{"align":"center","data":[{"name":"text","data":"10.285"}]}],[{"align":"center","data":[{"name":"text","data":"-50~-60"}]},{"align":"center","data":[{"name":"text","data":"11.833"}]},{"align":"center","data":[{"name":"text","data":"11.630"}]},{"align":"center","data":[{"name":"text","data":"10.289"}]}],[{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"-60~-66.6"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"11.931"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"11.533"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"10.432"}]}]],"foot":[]}]}},{"name":"p","data":[{"name":"text","data":"材料应变量和负载扭矩之间的关系如"},{"name":"xref","data":{"text":"图 8","type":"fig","rid":"Figure8","data":[{"name":"text","data":"图 8"}]}},{"name":"text","data":"所示，从图中可以看出，随着环境温度的降低，材料尺寸和负载扭矩的变化趋势是一致的，随着材料收缩量的不断增大，负载扭矩也不断增加。此外，当环境温度低于-60 ℃之后，材料的收缩量和负载扭矩均发生了较为明显的改变。因此，材料伸缩量和负载扭矩之间具有紧密的相关性。"}]},{"name":"fig","data":{"id":"Figure8","caption":[{"lang":"zh","label":[{"name":"text","data":"图8"}],"title":[{"name":"text","data":"应变量与负载关系曲线"}]},{"lang":"en","label":[{"name":"text","data":"Fig 8"}],"title":[{"name":"text","data":"Strain "},{"name":"italic","data":[{"name":"text","data":"vs."}]},{"name":"text","data":" Load"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707148&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707148&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1707148&type=middle"}]}}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"5"}],"title":[{"name":"text","data":"结论"}],"level":"1","id":"s5"}},{"name":"p","data":[{"name":"text","data":"望远镜负载扭矩随着温度的降低而增大，试验测试得出低温下的负载扭矩是常温下负载扭矩的6.67倍。深入研究分析了润滑剂和材料的热膨胀系数对负载扭矩的影响。实验结果表明：润滑脂黏度随温度的降低而增加，使负载扭矩增大同时具有非线性特性，低温环境下去除润滑脂可以减小负载扭矩。随着温度的降低，由热膨胀系数引起的材料缩短量最大达到了960 "},{"name":"italic","data":[{"name":"text","data":"με"}]},{"name":"text","data":"，轴承间隙变小，导致滚动轴承的摩擦扭矩增加。在温度下降的过程中，-60 ℃之前，材料的热膨胀系数基本保持不变，当环境温度低于-60 ℃时，材料的热膨胀系数明显增大。为了保证设备平稳可靠工作，在温度变化较大且温度较低的环境时，在不影响精度的前提下，尽量加大轴承的游隙。此外，轴承材料应选择热膨胀系数小的材料，轴承的支撑材料尽量选择和轴承材料膨胀系数相近的材料。"}]}]}],"footnote":[],"reflist":{"title":[{"name":"text","data":"参考文献"}],"data":[{"id":"b1","label":"1","citation":[{"lang":"zh","text":[{"name":"text","data":"何秋生, 路瑶, 苑伟华, 等.应用于伺服系统的改进摩擦模型[J].机床与液压, 2015, 43(11):148-151."}]},{"lang":"en","text":[{"name":"text","data":"HE Q SH, LU Y, YUAN W H, "},{"name":"italic","data":[{"name":"text","data":"et al"}]},{"name":"text","data":".. 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